aenorm 72

Econometric Game 2011: Using Genetic Markers

as Instruments

This edition:

72 vol. 19aug ‘11

Maulding the Method of Moments into Kinky Least Squares

Interview with professor Frank Windmeijer

A New Quality Indicator for Survey Response

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AENORM vol. 19 (72) August 2011 1

Causal Inference

Colofon

Chief EditorMyrna Hennequin

Editorial BoardMyrna HennequinDaan Oosterbaan

Editorial StaffLucas OosterbaanAnnelieke BallerDianne KapteinJan Nooren

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by: Frank Windmeijer

Last April it was my pleasure and privilege to be the case maker and member of the jury for the Econometric Game. The cases were designed jointly with Stephanie von Hinke Kessler Scholder and focused on determining the causal effects of maternal alcohol consumption during pregnancy on cognitive outcomes of the child.

The main task when we carry out causal inference is to distinguish between association and causation. This should clearly be the guiding principle of any econometric analysis, especially those which might inform public policy. Looking at simple correlations, we find that mothers who drink during pregnancy (especially wine) have children with higher cognitive scores. It is also easily established that mothers who drink wine are on average richer and better educated. We can then of course control for these factors, but there may be others, like parenting style, for which there are no measures in the available data.

So, how could one get reliable causal estimates? The gold standard, especially in the medical literature to determine the efficacy of a treatment or a drug, is to run a randomised controlled trial (RCT) where patients get randomly assigned to the treatment or control (placebo) group. In many economic applications it is difficult, expensive or unethical to do an RCT. We cannot randomly assign expectant mothers to drinking alcohol! However, field experiments are becoming increasingly popular, especially in development economics, with individuals randomly assigned to e.g. different saving or investment instruments.

Economists often analyse data from observational studies where treatment is not assigned, but chosen by the individual. The use of Instrumental Variables (IV) and associated estimation techniques could then be a way forward to establish the causal effects. An IV acts like a random assignment device, it does affect treatment, but not the outcome other than via the treatment. In the cases for the Econometric Game, we used mothers’ genetic markers that are known to affect alcohol consumption as instruments for their drinking behaviour. In this edition of AENORM you will find an article discussing the use of genetic markers as IVs and an article by the winning team from Maastricht presenting their analyses.

The world of causal inference is a fascinating one. It applies to many sciences: e.g. economics, medicine, epidemiology, physics, engineering and psychology. I mentioned RCTs, field experiments and IVs, but there are also natural experiments, potential outcomes, counterfactuals, structural models, weak instruments, LATEs and the field of behavioural economics to name a few more. I recommend reading the recent discussions within economics between Professors Deaton, Heckman and Imbens on the pros and cons of various approaches. The issues are important and not just confined to the traditional economic domains of returns to education or training. For the design of policies and interventions one needs to first establish the correct evidence on what works.

The Econometric Game is a unique and highly regarded event for teams of econometricians from all over the world. I would like to thank the VSAE Committee for organising the event in such a fabulous and professional way. And you, reader of this AENORM, should feel proud to be part of an institution that organises such a prestigious Game!

“The world is richer in associations than meanings, and it is the part of wisdom to differentiate the two.” — John Barth, novelist.

2 AENORM vol. 19 (72) August 2011

00 vol. 00m. y.72 vol. 19

aug ‘11

04

In this issue of Aenorm, we present four articles related to the Econometric Game 2011. The first article is a summary of the winning report of Maastricht University. On the first day of the Econometric Game 2011, teams were asked to investigate the causal effect of alcohol consumption during pregnancy on the child’s cognitive skills. On the second day, a more in-depth analysis of the same question was complemented by an examination of the causal effect of obesity on the child’s social life (i.e., the incidence of peer problems). In both cases, problems of endogeneity called for the use of genetic markers as instruments.

13

Recent developments in the science of genetics have dramatically reduced the cost of obtaining genetic data. This has led many cohort studies and other surveys, including those often used by social scientists, to collect bio-samples and extract genetic data. But what can genetic information offer social scientists? Genetic data can be used to test causal hypotheses, for example using an Instrumental Variables (IV) approach. The case for the Econometric Game 2011 involved one of the potential uses of genetic information.

08

Frank Windmeijer is a professor of Econometrics at the University of Bristol since July 2005. At the Econometric Game 2011, 25 teams from universities all over the world dig in deep into a subject which Windmeijer has been working on for several years. In this interview, he talks about statistics with DNA-samples, econometrics-studies in the Netherlands and being occupied in England.

by: Tim Cardol

Interview with Professor Frank Windmeijer

This article is based on the presentation of Professor Kiviet during the Econometric Game Congress. The major challenge of econometrics is assessing the essentials of relationships between empirical phenomena, where this has to be based on data which could not be collected from controlled experiments. This calls for inference procedures which can handle both exogenous and endogenous explanatory variables. In this article is demonstrated that some of the crucial but statistically unverifiable assumptions can be replaced by others, in order to make inferences more credible, robust, efficient and accurate.

by: Stephanie von Hinke Kessler Scholder, Neil Davies and Frank Windmeijer

Genetic Information: Potential Uses for Economics and Social Science Research

by: Jan F. Kiviet


by: Thomas Götz and Daniel Pollmann

Econometric Game 2011: Using Genetic Markers as Instruments

11

More Time for Research in England


BSc - Recommended for readers of Bachelor-level

MSc - Recommended for readers of Master-level

PhD - Recommended for readers of PhD-level

Facultive 36

35Puzzle

29

This article presents a method to estimate the volatility at any time within a trading day using high frequency price data. The method is not hindered by the occurrence of (infrequent) jumps, (frequent) microstructure noise, daily recurring patterns in the variance, or leverage effects. The resulting spot volatility path allows to track variation of prices at short intraday horizons, or to test for jump effects related to e.g. news announcements. The authors present an empirical illustration of spot volatility estimation and jump testing for the intraday EUR/USD exchange rate.

Nonresponse in sample surveys is the phenomenon that elements (e.g. businesses, persons, or households) selected in the sample do not provide the requested information, or that the provided information is useless. The situation in which all requested information on an element is missing (the questionnaire remains empty), is called unit nonresponse. When only answers on some questions are missing, this is referred to as item nonresponse. This article focuses on the analysis of unit nonresponse and its impact on the quality of survey statistics. The authors give an introduction to indicators that can be used to assess and evaulate the impact of nonresponse, so-called R-indicators.

by: Jelke Bethlehem, Fannie Cobben and Barry Schouten


Under the current rules pension funds must value their pension liabilities using market-value interest rates. This is in contrary to the fixed interest rate that was used before. The average funding level drastically declined due to the credit crisis. The developments of the interest rates had major consequences for the value of pension rights. This article explains which effects market-value interest rates have on the Dutch pension market.

The Effect of Interest Rate Changes on the Dutch Pension Market

by: Dirk Korbee and Arjen Pasma

by: Charles S. Bos and Pawel Janus

Spot Volatility of High Frequency Data

Sovereign credit risk analysis gained renewed interest after the European sovereign debt crisis, as it showed that even high-rated sovereigns can be vulnerable. This article examines the credit risk information in the bond- and CDS market for emerging economies. Four main conclusions: the markets price credit risk accurately; the bond market is the most efficient; spreads in the CDS market are driven by global factors and the previous spreads (historical prices); and credit ratings do not contain more information than historical prices.

by: Marcel Weernink

Market Based Indicators of Sovereign Credit RiskAn Examination of the Bond- and CDS Market in Emerging Economies

17

22

24


Econometrics

Introduction

The impact of excessive exposure to maternal alcohol consumption on an unborn is widely discussed in the literature. RCOG (2006) report various adverse outcomes such as disordered fetal growth, an increased susceptibility to disease in adult life and congenital malformations, while other authors are more skeptical about the effect on different sorts of outcomes, such as cognitive ability, and point to the issue of confounding. Unobserved factors such as habits or self-discipline of the mother may influence both maternal drinking behavior and the mental capacity of the child, resulting in correlation rather than causation. The ongoing debate about the connection between alcohol consumption and possibly drastic health effects on the child calls for a detailed analysis of their causal relationship.

The link between children’s being overweight and the incidence of peer problems is also ambiguous due to bidirectional causality (reverse causal relationship) as well as confounding. On the one hand, overweight children might be bullied and made fun of, while on the other hand, children could eat excessively out of frustration about a lack of social integration.

Data

In order to shed light on the issues described above, we take data from the Avon Longitudinal Study of Parents and Children (ALSPAC) on a cohort of children born in a UK region in 1991 and 1992 (Golding et al., 2001). The outcome variable on the first day was the children’s exam score on the national Key Stage 2 test (KS2) taken at age 11. On the second day, the dependent variable for the effect of alcohol intake was an indicator for the attainment of level 5 or higher on the KS2, while for obesity, it was a binary variable for the incidence of peer problems at age 10. Next to the amounts of maternal alcohol intake at different points of gestation and the prevalence of obesity, as measured by BMI at age 7, explanatory variables include demographic and socioeconomic characteristics of mother and father.

Endogeneity and Mendelian randomization

If an unobserved variable affects both modifiable exposure (alcohol consumption or obesity) and outcome (cognitive skills or social life), confounding results in an endogeneity problem. These unobservables are often innate ability/intelligence and psychological or lifestyle factors. For instance, families who devote little attention to their children’s nutrition, leading to obesity, might similarly neglect the development of their offspring’s social skills, resulting in peer problems.

The usual approach is to conduct Instrumental Variable (IV) estimation, but where can we find suitable instruments? Recall the core assumptions of IV estimation:

• Independence of the potential outcomes and IV.• Exclusion: The IV influences the outcome only

indirectly through the exposure/treatment.• Validity: There is a causal effect of the IV on the

exposure.

On the first day of the Econometric Game 2011, teams were asked to investigate the causal effect of alcohol consumption during pregnancy on the child’s cognitive skills (measured by a standardized test at age 11). On the second day, a more in-depth analysis of the same question was complemented by an examination of the causal effect of obesity on the child’s social life (i.e., the incidence of peer problems). In both cases, problems of endogeneity called for the use of genetic markers as instruments under the concept of Mendelian randomization. However, since these instruments turned out to be weak, non-standard methods were necessary for consistent inference.

by: Thomas Götz and Daniel Pollmann

Econometric Game 2011: Using Genetic Markers as Instruments

Team Maastricht UniversitySarah Dahmann, who would like to study econometric applications in the area of international economics; Thomas Götz, who is working on non-stationary mixed-frequency time series; Daniel Pollmann, whose interests are microeconometrics, labor economics, and preference heterogeneity; Marc Schröder, who is interested in the game theoretic approach of mathematical economics; and Lei Wan, who is dealing with asymptotic theory and non-linear or non-stationary dynamic panels and time series.


Econometrics

Mendelian randomization circumvents the problem of confounding by employing a genetic variant as instrument for the modifiable exposure (Lawlor et al., 2008). It is based on Mendel’s Second Law, which states that a child’s genotype is randomly assigned at conception given the genotypes of the parents (Davey Smith and Ebrahim, 2003). Therefore, “at a population level [the genotype is] largely unrelated to the many socioeconomic and behavioral characteristics that are closely linked with each other” (von Hinke Kessler Scholder et al., 2010). Hence, given validity, the genetic variant affects the outcome only indirectly through its association with the modifiable exposure.

The genotype we employ to investigate the relationship between alcohol consumption during pregnancy and the child’s cognitive skills is the mother’s ADH1B; Zuccolo et al. (2009) show its validity as an instrument for prenatal alcohol exposure. Due to the negative effect of the genotype on a woman’s alcohol metabolism, which is particularly pronounced during pregnancy, mothers who possess it can be expected to drink only very moderately or abstain from alcohol altogether. For the relationship between obesity and peer problems we use two genotypes of the child, FTO and MC4R, as discussed by von Hinke Kessler Scholder et al. (2010). After checking the validity of the relevant assumptions, both genotypes were considered suitable for our purposes. Lawlor et al. (2008) mention additional conditions specific to the use of genetic markers as instruments:

• The association with the modifiable exposure should not be weak in the sense that it only explains little of the variation in the risk factor (this issue is revisited later).

• The genotype is allowed to possess an association with the outcome only indirectly through the exposure of interest (exclusion), not even through another genotype “located closely” to the one under consideration (linkage disequilibrium).

• The causal effect should not merely be due to different frequencies of the genetic variant in several subpopulations (population stratification).

• Monotonicity: No one does the opposite of the assignment (in terms of the genotype), no matter the assignment. When considering alcohol consumption, e.g., it means that if a person does not have the rare genotype (associated with low amounts of alcohol consumption) and does not drink, it implies that this person would also not drink when having the rare gene.

Day 1: Weak instruments

Only about 5% of the mothers in our sample share the rare ADH1B allele, and so, the relationship between instrument and treatment is weak. This notion can be checked in the statistical sense by comparing the F-statistic from a regression of treatment on instrument

to the critical values in Stock and Yogo (2002). As shown by Nelson and Startz (1990a, 1990b), in the presence of weak instruments and for finite samples, the 2SLS estimator is biased towards the probability limit of the OLS estimator, which itself is biased in the presence of endogeneity; furthermore, the standard normal approximation is not applicable. The weakness may stem from a lack of identification or correlation. As stated above, the low frequency of the particular genotype in our sample leads to a low degree of correlation with drinking behavior for the whole sample. In terms of identification, we are rather doubtful as to our ability to explain varying amounts of consumption with a binary instrument. We therefore restrict our analysis to a binary indicator for the consumption of alcohol. Unfortunately, this rules out investigating possibly non-linear effects at different levels of consumption.

Table 1 reports the results from three different estimation methods: OLS, ignoring the presence of endogeneity, 2SLS, which is subject to the issues described above, and Fuller-1 estimation. The latter is best unbiased to second order, partially robust to weakness of instruments and allows inference based on the normal asymptotic approximation (Stock et al., 2002). Results for alcohol consumption at 18 and 32 weeks gestation are qualitatively similar to those at 8 and are therefore omitted. While OLS suggests no negative effect of maternal alcohol intake on the child’s cognitive ability, 2SLS and Fuller-1 do, albeit at different levels of

Table 1. The effect of alcohol consumption on cognitive skills (dependent variable: KS2 score).

Coefficient estimate (t-statistic)

OLS 2SLS Fuller-1

Alcohol8 0.126 -12.548** -11.321* (0.52) (-2.09) (-1.72)Mother’s age 0.257 0.485 0.476 (1.08) (1.22) (1.37)Mother’s age sq. -0.004 -0.006 -0.006 (-0.94) (-0.84) (-0.96)Girl 0.683*** 0.479 0.512 (3.04) (1.32) (1.40)Mother’s 2.458*** 2.882*** 2.861***education (16.83) (12.08) (12.16)Father’s class -1.126*** -1.150*** -1.139*** (-11.48) (-7.27) (-7.46)Log income 2.245*** 2.705*** 2.650*** (8.02) (5.42) (5.33)Age at KS2 0.289*** 0.374*** 0.367*** (9.68) (6.63) (6.44)Constant 44.272*** 28.479*** 29.622*** (8.20) (2.78) (3.01)N 5,173 3,683 3,683

*/**/*** denote significance at 10%/5%/1% level


Econometrics

significance. The difference between OLS and the two alternatives can very likely be attributed to endogeneity, the presence of which is suggested by a Durbin-Wu-Hausman test, consistent even in the presence of weak instruments (Tchatoka and Dufour, 2010). Interestingly, in spite of the bias of 2SLS towards the OLS estimator, the Fuller-1 coefficient appears to be slightly closer to it as measured in standard deviations. The coefficients for 2SLS and Fuller-1 seem very large and possibly overstate the true effect, as the outcome variable has a mean of around 100 with a standard deviation around 10.

It is surprising that OLS appears to be biased towards no effect. We expected that due to confounding, mothers with unfavorable unobservables would also be more likely to drink during pregnancy, such that OLS would overstate the true effect. One interesting remaining issue is the differential impact of beer and wine. Unfortunately, given only one instrument, we cannot simultaneously identify consumption of both. While parental income and education are powerful predictors of the choice between beer and wine, the results in table 1 show that they are very unlikely to be exogenous with respect to the outcome, which makes us very skeptical regarding their use as instruments. When experimenting with them, we find that beer has a detrimental impact, with the opposite result for wine.

Day 2: Binary outcomes and LATE

If the outcome is binary (i.e., attainment of a specific level on the KS2, incidence of peer problems), the average causal effect is not point-identified. However, under

certain conditions, it is possible to estimate a so-called local average treatment effect (LATE); with an additional monotonicity assumption similar to the one discussed above, the IV estimator will estimate the LATE even if treatment effects are heterogeneous across individuals (Imbens and Angrist, 1994; Angrist et al., 1996). The LATE is defined as the average treatment effect for those individuals whose treatment (Di ) is switched on because of the instrument (Zi ) and can be shown to estimate the counterfactual effect of the treatment (Y1i - Y0i ):

1 0 1 0[ | 1] [ | 0]

[ |[ | 1] [ | 0]

i i i ii i i i

i i i i

E Y Z E Y ZE Y Y D D

E D Z E D Z= − =

= − >= − =

]

The availability of multiple instruments in the obesity analysis introduces some interesting refinements. Consistent with the LATE framework, we use binary instruments by creating indicator variables based on a three-by-three cross table of the different possible values taken on by each of the two genotypes. Since these are mutually exclusive, IV estimation results in an estimator for the LATE which is “a linear combination of the instrument-specific LATEs using the instruments one at a time” (Angrist and Pischke, 2008); because BMI is a continuous rather than dichotomous variable, we in fact estimate a “weighted average of unit causal effects”.

In a binary model, by construction, we face heteroskedasticity of the error terms, rendering the previous Fuller estimator inconsistent. While a 2-step GMM estimator is efficient under heteroskedasticity and provides consistent statistics, it is biased given weak instruments. Again, using the F-statistic from a first-stage

Table 2. The effect of alcohol consumption on cognitive skills (dependent variable: level 5 or higher on KS2). Coefficient estimate (t-statistic)

OLS 2-step GMM LRR

Alcohol8 0.007 -0.854* -4.327*** (0.48) (-1.91) (-6.50)Mother’s age 0.003* 0.011** 0.024** (1.69) (2.52) (2.41)Girl -0.016 -0.025 -0.18** (-1.26) (-1.08) (-2.30)Mother’s 0.123*** 0.147*** 0.263***education (14.65) (9.38) (5.64)Father’s class -0.043*** -0.049*** -0.165*** (-7.65) (-5.10) (-4.80)Log income 0.091*** 0.113*** 0.336*** (5.77) (3.65) (3.17)Constant -0.181* -0.309* (-1.91) (-1.87) N 5,377 3,827 3,827

Note: Age at KS2 omitted as LRR proved compu-tationally infeasible.*/**/*** denote significance at 10%/5%/1% level

Table 3. The effect of BMI on peer problems (dependent variable: incidence of peer problems). Coefficient estimate (t-statistic)

OLS 2-step GMM LRR

BMI7 0.018*** 0.035 0.045 (5.15) (1.01) (0.46)Mother’s age -0.002 -0.002 -0.007 (-1.17) (-1.13) (-1.12)Girl -0.034** -0.039** -0.132** (-2.53) (-2.42) (-2.32)Mother’s 0.013 0.015 0.049***education (1.48) (1.56) (1.33)Father’s class -0.003 -0.003 -0.011 (-0.41) (-0.45) (-0.42)Log income -0.091*** -0.092*** -0.357*** (-5.15) (-5.16) (-4.96)Constant 0.506*** 0.228 (4.19) (0.40) N 3,955 3,955 3,955

Note: Age at KS2 omitted as LRR proved compu-tationally infeasible.*/**/*** denote significance at 10%/5%/1% level


Econometrics

regression, we are unable to reject the null of weakness at most size levels and in most specifications; an Anderson LM test, however, rejects the null of underidentification. Given this evidence, we expect heteroskedasticity to be a larger issue than weakness of instruments, and we therefore work with the 2-step GMM estimator. As a robustness check, we carry out local risk ratio (LRR) estimation on an exponential model in the spirit of Mullahy (1997).

As reported in table 2, both 2-step GMM and LRR estimation yield a negative effect of maternal alcohol consumption on a child’s attaining at least level 5 on the KS2. While the coefficient estimates are not directly comparable in magnitude, the significance appears much clearer in the LRR framework. This stands in contrast to the OLS results, which, in line with the results of the day before, suggest no significant effect.

For the effect of obesity on peer problems, all results are reported in table 3. Neither 2-step GMM nor LRR estimation suggest any significant effect, while simple OLS estimation might (mis)lead one into finding a significant positive effect.

Conclusion

The results of both days illustrate the importance of controlling for endogeneity. To this end, Mendelian randomization makes intriguing use of a natural experiment in its purest form. However, new challenges, many of which we have spared the reader of, arise, such as weakness of instruments and heteroskedasticity.

As good as the food was during the Econometric Game, we were simply too busy working to conduct an actual randomized controlled trial on the social effects of obesity. However, we like to believe that alcohol consumption did not prove detrimental to our cognitive abilities and thank the organizers for the celebratory bottle of champagne.

References

Angrist, J.D. and Pischke, J.-S. Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton: Princeton University Press, 2008. Print.

Angrist, J. D., Imbens, G. W., and Rubin, D.B. “Identification of causal effects using Instrumental Variables.” Journal of the American Statistical Association 91 (1996): 444-55.

Davey Smith, G. and Ebrahim, S. “Mendelian randomization: Can genetic epidemiology contribute to understanding environmental determinants of disease?” International Journal of Epidemiology 32 (2003): 1-22.

Golding, J., Pembrey, M., and Jones, R. “ALSPAC - The Avon Longitudinal Study of Parents And Children:

I. Study methodology.” Pediatric and Perinatal Epidemiology 15 (2001): 74-87.

Imbens, G. W. and Angrist, J. D. “Identification and Estimation of Local Average Treatment Effects.” Econometrica 62 (1994): 467-75.

Lawlor, D. A., Harbord, R. M., Sterne, J. A. C., Timpson, N., and Smith, G. D. “Mendelian randomization: Using genes as instruments for making causal inferences in epidemiology.” Statistics in Medicine 27 (2008): 1133-63.

Mullahy, J. “Instrumental-variable estimation of count data models: Applications to models of cigarette smoking behavior.” The Review of Economics and Statistics 79 (1997): 586-93.

Nelson, C. R. and Startz, R. “The distribution of the instrumental variables estimator and its t-ratio when the instrument is a poor one.” Journal of Business 63 (1990a): 125-40.

Nelson, C. R. and Startz, R. “Some further results on the exact small sample properties of the instrumental variables estimator.” Econometrica 58 (1990b): 967-76.

RCOG. “Alcohol consumption and the outcomes of pregnancy.” RCOG Statement 5 (2006), Royal College of Obstetricians and Gynaecologists, London.

Stock, J. H., Wright, J.H., and Yogo, M. “A survey of weak instruments and weak identification in Generalized Method of Moments.” Journal of Business & Economic Statistics 20 (2002): 518-29.

Stock, J. H. and Yogo, M. “Testing for Weak Instruments in Linear IV Regression.” NBER Technical Working Papers 0284 (2002), National Bureau of Economic Research, Inc.

Tchatoka, F. D. and Dufour, J.-M. “Testing for weak instruments in linear IV regression.” Unpublished (2010).

Von Hinke Kessler Scholder, S., Smith, G. D., Lawlor, D. A., Propper, C., and Windmeijer, F. “Genetic markers as instrumental variables: an application to child fat mass and academic achievement.” The Centre for Market and Public Organisation 10/229 (2010), Department of Economics, University of Bristol, UK.

Zuccolo, L., Fitz-Simon, N., Gray, R., Ring, S. M., Sayal, K., Smith, G. D., and Lewis, S. J. “A non-synonymous variant in ADH1B is strongly associated with prenatal alcohol use in a European sample of pregnant women.” Human Molecular Genetics 18 (2009): 4457-66.


Since 1992 he has not been occupied in the Netherlands, but for the Econometric Game 2011 he gladly makes an exception. Frank Windmeijer of Bristol University about statistics with DNA-samples, econometrics-studies in the Netherlands and being occupied in England. “Great Britain has a long and rich history of academic endeavours. Working there is very agreeable.”

At the Econometric Game 2011, held in an oecumenic church at the Prinsengracht, Amsterdam, 25 teams from universities all over the world dig in deep into a subject which Frank Windmeijer has been working on for several years. At Bristol University he studies the causal effects of maternal alcohol consumption during pregnancy on cognitive outcomes of the child. He uses genetic markers as instruments to comprehend drinking habits.

In what way does the Econometric Game contribute to your study?

Today, I too have been doing a quite a lot of figures. Genetic markers do have a remarkable forecasting spell in determining one drink more or less, but there is very little accuracy in determining a link between alcohol consumption and cognitive outcomes of the child. One does find a link between specific genes and alcohol usage, but the question is if and how one can incorporate these genetic markers as instruments in an econometric survey.

I’m hoping that the participants will evolve an opinion based on the given examples.

And what is your opinion on using genes in econometrics?

So far utilising genes turns out not to be a strong instrument. It influences behaviour too little to have forecasting possibilities, forecasting alcohol usage founded on the genes is rather obvious, but a comprenhensive link between cognitive scores and the gene is too unclear to be confident about it.

You are involved in other applied studies. Could you elaborate on that?

Well, I’m not solely occupied at Bristol University, but also with several research institutions in Britain. Colleagues of the Centre for Market and Public Organisation are conducting surveys to the effect of rankings of British schools. Does it do any good? As it turns out schools did improve as they were being scrutinized.

I myself participated with another survey as instigated by a ‘Blair Adminstration’ policy. It’s goal was to reduce waiting time in hospitals. We expected reducement in quality and did comparative surveys in Scotland where no reducement policy is at hand. We studied ‘unintended

by: Tim Cardol

Interview with Professor Frank Windmeijer

Frank Windmeijer

Frank Windmeijer is a professor of Econometrics at the University of Bristol since July 2005. After completion of his PhD on goodness-of-fit measures at the University of Amsterdam in 1992, he was first a visiting lecturer at the Australian National University, before moving to London in 1994. There he first held a Marie Curie fellowship at University College London and then became a senior research fellow at the Institute for Fiscal Studies and a co-director of the Centre for Microdata Methods and Practice. His best known econometrics contribution is the finite sample correction to the two-step GMM standard errors, as programmed up in e.g. Stata. He has further contributed to various applied projects, including analysing demand for health care. In recent years he has started to collaborate with colleagues in the Social Medicine department, assessing the usefulness of genetic markers as instruments for e.g. obesity or alcohol intake.

Frank Windmeijer was the case maker and member of the jury for the Econometric Game 2011. This interview is a translation of the interview held by Tim Cardol for the Dutch online magazine ScienceGuide (www.scienceguide.nl).

More Time for Research in England


consquences’ such as increased number of deceased in hospitals. In contrast to our expectations it turned out that in England improvements were noticed and waiting times reduced. Overall results were better than in Scotland, where no reducement policy was implanted.

Since 1994 you are occupied in England, at first in London, and afterwards in Bristol. What’s the attraction?

Well, my wife is English, a main reason, but I have to admit that in England there is a pleasing academic environment. Great Britain has a great history and a rich academic setting. Research has a very prominent stature, doing thorough research is obligatory.

In what way does that manifest itself?Every seven to eight years a ‘Research Assesment

Exercise’ is conducted in England. Each scientist is asked to hand in four of its best papers to be reviewed by a panel and subsequentially ranked in its field. Thus all economy faculties are compared. In all, funding will be directed accordingly. Result is that much effort is done to attract proficient scientists, so academic England is rather research minded.

Comparing with situation in the Netherlands, how positive are you?

In the Netherlands there are just less universities and the degree of levelness is higher. At least that is what I experienced, but I left in 1992. In Great Britain otherwise competive ranking is very prominent. A while ago all highschools have been promoted to university status. The conducted ranking does show the difference between ‘classical universities’, as typical research prone, and the others.

In the Netherlands that should not happen as far as I can tell. Colleges should not become universities. Universities have their own place, colleges another, it’s common knowledge.

Here at the Econometric Game a team of your university is present. How about differences in quality in the field of econometrics between the Netherlands and Great Britain?

In Great Britain there are far few econometrcians than in the Netherlands. Econometics is no sole evocation on its own, just an integrated part of an economies study. In the Netherlands there is a strong trail in econometrics, naming Tinbergen who has had a very important impact. In Great Britain specializations on local scale are more common. In Bristol there is the ‘Centre for Structural Econometrics’ and in that field rather specialized.

Result of its rooting, econometrics is well taught in the Netherlands. One should pay attention that it should not suffer from lack of research. In Great Britain one usually has more opportunity for research. Important is to maintain the right balance. If one teaches a lot and sustains all its apparent administration, subsequentially

one’s research will suffer. That is in my opinion what more or less is going on in the Netherlands. The teaching is of high standard, but eventually research may suffer.

These differences, will they show up at the Econometric Game?

I have no idea. I am rather curious, coming dinner we are to discuss 25 works, 10 of them shall start a next assignment tomorrow. Eventually of these 10 the top 3 will be elected.

The Econometric Game 2011 was finally won by the team of Maastricht University.

Are you interested in being in the editorialstaff and having your name in the colofon?

If the answer to the question above is yes, please send an e-mail to the chief editor at

[email protected].

The staff of Aenorm is looking for people who like to:

- find or write articles to publish in Aenorm; - take interviews for Aenorm; - make summaries of (in)famous articles; - or maintain the Aenorm website.

To be in de editorial board, you do not necessarily have to live in the Netherlands.

69vol.18

dec ‘

71vol. 19

may ‘11

70vol. 18

dec ‘1072

vol. 19

aug ‘11


Econometrics

Introduction

Our genome influences many human features – from physical characteristics, such as height, to behaviour such as alcohol consumption, and traits that are more difficult to measure, like risk preferences. One way to study the influence of our genome on these characteristics is to calculate their heritability. This is defined as the proportion of the total variation in the characteristic that is due to genetic differences.

Heritability studies use statistical techniques to estimate this proportion. If certain characteristics of interest to social scientists are found to be heritable, we may then wish to examine and understand the specific underlying differences in DNA and the genetic mechanism that can explain this heterogeneity across individuals.

One approach to identify specific DNA locations that associate with a behaviour or trait of interest is the use of genome wide association studies (GWAS). These studies can relate up to 2.5 million genetic variants to the characteristic of interest. The information and genetic data obtained from these studies can then be used to test further causal hypotheses, for example using an Instrumental Variables (IV) approach.

Mendelian Randomization

We know that the allocation of genes from parents to offspring is random, as shown by Gregor Mendel (1822-84) in his study of the inheritance of traits in pea plants. In addition, studies have also shown that individuals’ genes are unlikely to be related to their background characteristics, such as socio-economic position, life expectancy or income. In fact, the term ‘Mendelian randomization’ refers to studies that exploit this random assignment of individuals’ genomes (Davey Smith and Ebrahim, 2003).

An Application: Prenatal Alcohol Con-sumption and Child Academic Attainment

Mendelian randomization uses the random assignment of genes to study the effects of a particular characteristic on an outcome of interest. The case for the 2011 Econometric Game involved using the (maternal) alcohol metabolism gene ADH1B as an instrumental variable for maternal prenatal alcohol consumption, to explore the effect of maternal alcohol intake during pregnancy on children’s academic achievement. In other words, the participants used the genetic variant ADH1B to explain variation in maternal alcohol consumption. This variation was then related to her child’s academic attainment to investigate the effect of maternal prenatal alcohol intake on children’s educational outcomes.

It may seem counterintuitive to use ADH1B to predict differences in maternal alcohol intake, rather than measuring alcohol intake itself. But there are several crucial advantages to this approach. The main one being that, unlike actual alcohol consumption, ADH1B is unlikely to be related to other behavioural, social and physiological factors that may confound the association between maternal alcohol intake and the child’s academic

Recent developments in the science of genetics have dramatically reduced the cost of obtaining genetic data. This has led many cohort studies and other surveys, including those often used by social scientists, to collect bio-samples and extract genetic data. But what can genetic information offer social scientists?

by: Stephanie von Hinke Kessler Scholder, Neil Davies and Frank Windmeijer

Genetic Information: Potential Uses for Economics and Social Science Research

Stephanie von Hinke Kessler Scholder, Neil Davies and Frank WindmeijerStephanie von Hinke Kessler Scholder is a post-doctoral research fellow at Imperial College London and a research associate at the CMPO, University of Bristol. Neil Davies is a post-graduate research student in the School of Social and Community Medicine, University of Bristol.

Frank Windmeijer is Professor of Econometrics in the School of Economics, Finance and Management, University of Bristol.


Econometrics

achievement. This means that if ADH1B is used to predict alcohol consumption, it is unlikely to be confounded with such factors.

The Avon Longitudinal Study of Parents and Children (ALSPAC) shows a strong positive association between maternal prenatal alcohol consumption and the child’s academic performance. This would suggest that alcohol consumption is good for the child’s academic development. However, the data also show a strong socio-economic gradient in drinking: the higher social classes and higher educated mothers are more likely to drink during pregnancy. Although we can control for some of these characteristics, we are unlikely to be able to control for all such confounders. Hence, simple least squares regression techniques are unlikely to estimate the causal effects of maternal alcohol intake on child development. We therefore turn to IV.

Unlike maternal alcohol intake, the genetic variant ADH1B is unlikely to be related to these background characteristics such as social class or maternal education. The use of ADH1B as an instrumental variable for maternal alcohol intake can therefore account for the endogeneity of maternal alcohol consumption. In contrast to the OLS findings, the IV approach shows consistent and large negative effects of maternal alcohol consumption on child academic achievement.

Potential Limitations of Mendelian Randomization

This shows that the use of genetic information in IV studies potentially allows researchers to explore causal research questions that are difficult or perhaps impossible to answer in observational studies. The advantage of Mendelian randomization lies in avoiding the confounding factors that often complicate the interpretation of observational studies. But like all research methods, it has limitations that must be taken into account. One potential problem is the strength of the instrument. Genetic variants often explain only little variation in the phenotype of interest, leading to a problem of weak instruments. Furthermore, if the association between the genetic variant and the phenotype of interest has not been replicated in different independent samples, it should not be used as the instrumental variable, as the sample correlation may simply be due to measurement error or chance (von Hinke Kessler Scholder et al., 2010, 2011).

Another potential problem is that the frequencies with which genetic variants occur may differ across different populations, such as ethnic groups. This is also known as population stratification. For example, ADH1B is much more common among Asians than European populations. If there also is a systematic difference in academic performance between Asians and Europeans, the IV approach would estimate an association between alcohol consumption and child educational attainment without an

actual causal relationship. In addition, when genetic variants are passed on

from one generation to the next, they may be linked (or co-inherited) with other variants (also known as being in Linkage Disequilibrium). Similarly, variants may influence more than one characteristic (pleiotropy). These situations could invalidate the IV assumptions and therefore need careful consideration (Davey Smith, 2010; von Hinke Kessler Scholder et al., 2010, 2011).

Conclusion

These potential problems may re-introduce confounding factors. However, rapid developments in our understanding of the genome and in the functions of specific variants, as well as technological and statistical advances, may alleviate some of these problems. With that, they make Mendelian randomization an increasingly powerful method for economics, social science as well as medical and epidemiological research.

References

Davey Smith, G. and S. Ebrahim (2003). “Mendelian Randomization: Can Genetic Epidemiology Contribute to Understanding Environmental Determinants of Disease?” International Journal of Epidemiology, 32: 1-22.

Davey Smith, G. (2010). “Mendelian Randomization for Strengthening Causal Inference in Observational Studies: Application to Gene x Environment Interactions.” Perspectives on Psychological Science, 5: 527-45.

von Hinke Kessler Scholder, S., D.A. Lawlor, G. Davey Smith, C. Propper and F. Windmeijer. (2010). “Genetic Markers as Instrumental Variables: An Application to Child Fat Mass and Academic Achievement.” CMPO Working Paper, 10/229

von Hinke Kessler Scholder, S., D.A. Lawlor, G. Davey Smith, C. Propper and F. Windmeijer (2011). “Mendelian Randomization: The Use of Genes in Instrumental Variable Analyses.” Health Economics, 20(8).


Econometrics

A simple though unidentified model

Consider the two linear equations

(1)

(2)

which model two endogenous variables and for observations Let the random disturbances be such that and , with

, where and . We suppose that

(3)

So, in both equations the two variables , for which we may assume , are predetermined, or even exogenous. However, we have when

. Then the two variables are jointly dependent. The first equation is the structural (causal) relationship

for and the second is the reduced form equation for . The three coefficients of the structural equation (1)

are not identified by the two orthogonality conditions . We will clarify this and examine by

what alternative further restricting assumptions their identification can be achieved.

Continuing to use obvious notation for variances and covariances we easily obtain the following relationships between second moments

(4)

(5)

(6)

(7)

(8)

Note that by virtue of the Law of Large Numbers such second moments regarding observed variables can directly be estimated consistently by their sample equivalent. This is not the case for , simply because has not been observed. The equations (5) through (8)

do no longer contain such a covariance involving an unobserved disturbance term, because we did already substitute the four orthogonality conditions (3).

From the two equations (7) and (8) consistent estimators for the two reduced form coefficients and

directly follow. Denoting sample second moments by putting a hat on we find from

The major challenge of econometrics is assessing the essentials of relationships between empirical phenomena, where this has to be based on data which could not be collected from controlled experiments. This calls for inference procedures which can handle both exogenous and endogenous explanatory variables. For proper interpretation of econometric inference various assumptions of a technical statistical nature should hold, whereas for some of these conditions their validity cannot be corroborated. Therefore, they simply have to be adopted, either on the basis of conventions or other often highly subjective convictions. In this note we demonstrate that some of these crucial but statistically unverifiable assumptions can be replaced by others, in order to make inferences not only more credible, but by the same stroke more robust, efficient and accurate as well.

by: Jan F. Kiviet


Jan F. KivietJan Kiviet started as a student in econometrics at the University of Amsterdam in 1966. After graduation in 1974 he became lecturer at UvA. He obtained his PhD in 1987 and was appointed full professor of econometrics in 1989. Commencing July 2011 his major occupation will be at Nanyang Technological University in Singapore. His research has a focus in improving econometric inference for dynamic and simultaneous relationships, especially for panel data models. Since 2009 he is an elected member of the Royal Netherlands Academy of Arts and Sciences.


Econometrics

that

(9)

where the matrix Z and vector are defined in the obvious way. Hence, as is well-known, reduced form coefficients are identified and can be estimated consistently by the method of moments (MM), which in this case is equivalent to least-squares (LS). From yet another equation in second moments,

(10)

we easily find a consistent MM estimator for ,

(11)

Due to the presence of the unkown term , identifying , and and obtaining consistent estimators for them

from the three equations (4), (5) and (6) is only possible by incorporating extra information. We will first review three options for this that have been discussed in the econometric literature for over half a century already, and next two further options, which have been suggested only very recently. We shall also try to indicate the advantages and disadvantages of these various approaches with respect to what in our opinion should be the major aspirations in econometrics.

Inference aspirations

In econometrics we want our inferences to be: credible, robust, efficient and accurate. These four qualities refer to the following. Although we have to accept that econometric inferences will be based on particular assumptions that simply have to be adopted, which neither can be imposed by brute force nor be verified empirically, we nevertheless often have a choice regarding which assumptions to adopt, or whether to formulate them very strictly or less restrictively. While adopting purely hypothetical and rather abstract assumptions may provide – as it seems – a fertile starting point in producing inference in economic theory, it cannot serve empirical econometrics in the same way, simply because in that field the assumptions made should not be incompatible

with reality. Although employing sound econometric theory built on premises which do not hold for the data under study might still be labelled conditionally valid, it is at the same time misleading and of no practical use.

So, in econometrics both illusory and elusive assumptions should best be avoided as much as possible. Nevertheless, the extent of the credibility of the adopted restrictions will be determined largely by subjective preferences. It is obvious, though, that less binding assumptions are usually more credible. Designing inferences such that they apply to less binding assumptions also boosts robustness. Robustness as such refers to appropriateness of the inference technique under a wide set of assumptions. However, robustness usually comes with a price in terms of reduced efficiency. The asymptotic efficiency of inferences and their precision in finite samples is often expressed by measures such as (asymptotic) root mean squared error, (local) power of tests, or length of confidence intervals. Naturally, we will prefer the inference technique which achieves higher precision than its competitors, but self-evidently here we will as a rule face trade-off dilemmas between efficiency and robustness. Usually these cannot be enhanced both at the same time. Finally, we want our inferences to be accurate, by which we mean that they should fulfill their claimed precision. Hence, estimated standard errors of estimators should concur closely with the actual corresponding standard deviations, and the actual type I error probability of tests should be close to the nominal significance level aimed at, whereas the actual coverage probability of confidence sets should be close to their claimed confidence coefficient.

Regarding the classic simultaneous model, which we did set out above in simplified rudimentary form, and which has been studied intensively since World War II, it may seem almost impossible that a new and useful technique can still be added to the existing econometricians toolbox. Nonetheless, we will suggest one below, and claim that what we nicknamed kinky least squares (KLS) has a very high CREA-factor. Very often it creates jointly more Credibility, Robustness, Efficiency and Accuracy than the existing techniques.

Five routes towards identification

First we discuss three strategies that have been very well documented in the literature1 already, and next two that have been suggested only very recently. They all claim to allow consistent estimation of the coefficients of the structural equation for . Note that in practice what we denote here as the separate vectors of explanatory variables might actually be vectors including more than one variable. However, allowing for that would complicate the notation substantially, but

1 For a concise and easily accessible though rather complete overview of the merits and pitfalls of the standard

approaches, see Larcker and Rusticus (2010).


Econometrics

not lead to qualitatively very different results, although having an unequal number of elements in and would require some special attention. The five distinct routes towards identification that we are aware of are the following.

Assuming This restriction implies so that is predetermined. Then the structural equation can be estimated consistently by LS. Of course, if in fact , then simultaneity is neglected and the LS estimator is inconsistent2, which jeopardizes the accuracy of standard LS inference. Because the LS residuals are orthogonal to all the regressors by construction, it is impossible to use them to test the validity of the restriction

Such a test is only feasible when the reduced form equation has at least as many explanatory variables as the structural form equation. This requires that at least one exclusion restriction holds in the structural equation. However, according to established wisdom, such a restriction cannot be tested either. Hence, for this option it does not seem that its credibility is easily substantiated and hence its accuracy is often doubtful.

Assuming Note that our model is symmetric in and , so assuming would have similar consequences. If this exclusion restriction is valid then the two equations (5) and (6) contain two unknowns and direct application of MM yields

(12)

where X is the matrix with on the row. This is the well-known instrumental variables (IV) estimator (and in a more general setting we would have found the 2SLS estimator). It is consistent. However, when at least one of the instruments is weak, it will suffer from finite sample bias almost as severe as inconsistent LS and have very poor efficiency too. These problems aggravate, and the IV estimator becomes inconsistent, when the exclusion restriction is in fact invalid. Then has to be accommodated by the disturbance term with the effect that orthogonality of this implied disturbance and ceases to be a possibility. Because the equations (4) through (6) do not identify the exclusion restriction cannot be tested from them. Hence, any inference on and based on this restriction is not credible without strong supplementary (from external sources) evidence on its validity.

The exclusion restriction issue refers to the classic identification problem. Variable is only an effective instrument for endogenous explanatory variable if it has no direct effect on but only an indirect effect via . If the effect of

on is not very strong ( is relatively small), then the instrument is weak and both and are only weakly identified which results in poor efficiency plus poor accuracy. If then and are not identified, irrespective whether or not the exclusion restriction holds. The strength of the instruments can always be assessed by estimating the reduced form, but testing the exclusion restriction is in the present context impossible.

Extending the reduced form equation. Instead of imposing restrictions, one can also try to extend the information, by disentangling disturbance and exploiting (alleged?) explanatory variables earlier omitted from the reduced form equation. Then this may lead to an extra component in (2) with also an extra corresponding orthogonality condition. Assuming now that , whereas has coefficient zero in the structural equation, we can find consistent IV estimators for and from the three equations (5), (6) and

(13)

Whether this approach is effective hinges upon the strength of instrument and the credibility of its zero coefficient in the structural equation. As always, the strength can be measured, but it is likely to be poor, given that omission of this variable was first seen as acceptable. Again, the exclusion restriction is untestable (because in the present case it does not concern an overidentification restriction). Hence, faith in its credibility gained from other than statistical sources is again crucial. Note that this third and the second option have much in common, but attain identification from different starting positions.

Assuming If the exclusion restriction seems inappropriate, and one does no longer aim at estimating

because information on its value can be obtained from other sources, then estimates for and can be obtained directly from (5) and (6). This yields

(14)

Of course, this modified IV estimator is inconsistent when the assumption on is incorrect. However, such an assumption can be made more flexible, for instance, by assuming to be the realization of a random drawing. This approach, and some Bayesian extensions, have been put forward recently by Kraay (2011) and Timothy

2 More consequences for LS of neglected simultaneity are analyzed in Kiviet and Niemczyk (2010).


Econometrics

et al. (2011). Although they replace the often very incredible exclusion restriction by a possibly much less restrictive and therefore also more credible assumption on , the resulting efficiency and accuracy will still be highly dependent on the strength and the validity of the instruments.

Assuming . Yet another option is to make an assumption on the degree of simultaneity. This leads to a procedure which does not require to impose any untestable exclusion restrictions, and neither is its efficiency and accuracy dependent on the strength of instruments. More details are given in Kiviet (2011). The essentials are as follows. Defining the row of X now to contain and substituting

, the equations (4) through (6) yield

(15)

Here is the square root of the consistent estimator for given by

(16)

This estimator involves application of LS, which is next modified in such a way that the various moment equations are being respected, securing consistency. At first sight, it seems unfeasible, because it requires the value of the unobservable . But then any MM estimator, including IV, is actually unfeasible, because they are obtained by substituting , whereas is unobservable too (and in addition the exclusion restrictions it requires for just identification are untestable). So, estimator (15) is certainly not necessarily less credible than other MM estimators. Moreover, its credibility can be enhanced by extending the underlying adopted assumption to the interval .

Of course, the wider this interval is, the more robust though less efficient the resulting inference will be. We do admit that (15) is an odd estimator, and it is curious that LS after a modification produces a useful estimator of coefficients which under the usual notions are not even identified. However, making an interval assumption on the simultaneity has apparently sufficient identifying power. All in all, Kinky LS seems an appropriate name for this uncommon estimator.

Where does KLS lead to?

KLS based inference can only be used effectively in practice by exploiting the limiting distribution of estimator (15), provided this is also reasonably accurate for its properties in finite samples. In Kiviet (2011) initial results can be found which demonstrate that under normality of all the regressor variables and the structural disturbance, the expression for the limiting distribution of KLS is remarkably simple. Moreover, inference in finite samples proves to be highly accurate when built on the true value of the simultaneity coefficient. Already for moderately strong instruments it is more accurate and efficient than IV based inference, and especially so when the instruments are weak. KLS inference can be made more credible and more robust by extending the interval

. If the true value is in the interval this means that KLS inference will be too prudent (the coverage probability of confidence intervals is much higher than required) but can still often be more efficient than IV inference. Only when the true value of the simultaneity coefficient is not in the adopted interval KLS inference becomes inaccurate and may be worse than IV inference. Presently, work is underway to provide full proofs for cases with an arbitrary number of endogenous and exogenous regressors, supplemented with applications which will throw new light on established empirical results which are based on IV inference exploiting often weak and possibly even invalid instruments. In principle, it will then be possible to test the allegedly untestable exclusion restrictions by KLS!

References

Conley, G.C., Hansen, C.B., Rossi, P.E., 2011. Plausibly exogenous. Review of Economics and Statistics, forthcoming.

Kiviet, J.F., 2011. Identification and inference in a simultaneous equation under alternative information sets and sampling schemes. UvA-Econometrics Discussion Paper 2011/02.

Kiviet, J.F., Niemczyk, J., 2011. The asymptotic and finite sample (un)conditional distributions of OLS and simple IV in simultaneous equations. Journal of Computational Statistics and Data Analysis, forthcoming. (UvA-Econometrics Discussion Paper 2010/01).

Kraay, A., 2011. Instrumental variables regressions with uncertain exclusion restrictions: A Bayesian approach. Journal of Applied Econometrics, forthcoming.

Larcker, D.F., Rusticus, T.O., 2010. On the use of instrumental variables in accounting research. Journal of Accounting and Economics 49, 186-205.


Econometrics

Introduction

The Dutch State offers credit risk insurance1 in cases for which no insurance can be got from private parties. Basically, these are large, capital-intensive export contracts to buyers in emerging countries. During the underwriting of these contracts, it is essential to get a comprehensive view on the creditworthiness of the counterparties. Besides the usual approach, fundamental analysis, financial markets could be another source of credit risk information. For sovereign credit risk, the two main market indicators are the bond market and the credit default swap (CDS) market. In the bond market the difference in yield between the risky and the risk-free asset is the credit risk component. The CDS market explicitly prices credit risk, as a CDS contract states that the seller will pay to the buyer the face value of a bond of entity X in case of a credit event in exchange for a (semi-)annual spread payment. In this article bond credit yield

Sovereign credit risk analysis gained renewed interest after the European sovereign debt crisis, as it showed that even high-rated sovereigns can be vulnerable. This paper examined the credit risk information in the financial markets (bond- and CDS market) for emerging economies. Four main conclusions: (1) the markets price credit risk accurately; (2) the bond market is the most efficient; (3) spreads in the CDS market are driven by global factors and the previous spreads (historical prices); and (4) credit ratings do not contain more information than historical prices.

by: Marcel Weernink

Market Based Indicators of Sovereign Credit Risk

Marcel WeerninkMarcel Weernink (1987) studied the MSc in Economics at the University of Amsterdam. He also obtained his bachelor at the same university. This article is a summary of his master’s thesis written during an internship at the Dutch Ministry of Finance (Export Credit Insurance Division, part of the Foreign Financial Relations Directorate). He is supervised by prof. dr. van Wijnbergen and prof. dr. Guerriero, and at the Ministry of Finance by G. Lubbers and M. de Ruiter.

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Jan-06 Jul-06 Jan-07 Jul-07 Jan-08 Jul-08 Jan-09 Jul-09 Jan-10 Jul-10

basispoints

BrazilCDS spread

Bond credit spread

Figure 1. Graphs of historical bond- and CDS spreads.

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1 For more information on export credit insurance,

please see: “http://www.rijksoverheid.nl/onderwerpen/

internationaal-ondernemen/exportkredietverzekering”.

An Examination of the Bond- and CDS Market in Emerging Economies


Econometrics

spreads and CDS spreads are always annualized.Both the bond2- and CDS3 prices are extracted from

Bloomberg. The sample includes eight countries4: Brazil, China, Colombia, Mexico, Peru, the Philippines, Turkey and Venezuela. The sample period is 2006-2010 (five years, daily data); therefore it includes the recent financial crisis. The summary statistics of this sample are provided in table 1. A graphical representation for three of these countries is provided in figure 1, it clearly shows the influence of the crisis on the spreads.

Long-run relationship between the bond- and CDS market

A first question that arises is if the two markets price credit risk accurately. Theoretically one should expect that arbitrage forces the two markets to price credit risk equally (Duffie, 1999). The cash flows of a CDS contract can be constructed synthetically by shorting the risky bond and buying the risk-free bond. Although this relation suffers from some practical problems (e.g. transaction costs; counterparty risk), the equilibrium relationship between both markets is confirmed empirically (using the Johanson cointegration framework) for all countries, except Venezuela.

Credit risk price discovery

Another interesting question is whether the bond- or the CDS market is faster (more efficient) in pricing

credit risk. In developed countries, the CDS market is faster, as it is cheaper to take a position in a derivatives market than in a cash market. The empirical literature for emerging markets is less clear. To test for efficiency in price discovery, first a VECM (vector error correction model) is estimated5 following equation 1:

CDStBSt

= 1

2CDSt-1 - i - iBSt-1 +

1,j CDSt-jpj=1

2,j CDSt-j

pj=1

+ 1,j BSt-j

pj=1

2,j BSt-j

pj=1

+ 1,t

2,t

(1)

In equation 1, CDSt and BSt are the CDS spread and the bond credit spread at time t; the coefficients λ1 en λ2 measure the speed of the adjustment to price inconsistencies from the long-term trend. For all countries in the sample λ1 is significantly negative and λ2 is significantly positive, meaning that both the bond and the CDS market take part in the adjustment process. The size of the coefficients then tells which market leads the price discovery process.

The price discovery measures of Gonzalo and Granger (1995) (GG) and Hasbrouck (1995) (HAS) are both related to the relative sizes of the adjustment coefficients. The GG-measure is defined as the ratio of the speed of adjustment in the two markets, while the HAS-measure is based on the information value in the variance and covariance of the residuals. They are defined as stated below:

Table 1. Summary statistics data set.

Brazil China Colombia Mexico Peru Philippines Turkey Venezuela

Mean 150.48 63.55 169.96 126.95 155.98 203.09 224.55 829.62CDS Median 125.20 60.75 145.59 108.35 127.60 181.41 191.67 616.43spread Maximum 586.41 276.30 600.37 601.21 586.28 824.78 824.61 3239.28 Minimum 61.50 10.08 64.70 28.17 59.66 93.21 116.55 117.50 Observations 1293 1297 1292 1293 1301 1298 1295 1303

Mean 185.10 92.80 211.39 163.39 241.61 236.86 275.27 814.54Bond Median 159.90 78.72 179.67 147.92 206.63 208.77 231.29 712.84credit Maximum 646.69 323.86 734.70 594.63 625.93 810.23 1043.01 2142.70spread Minimum 58.90 16.18 58.27 53.02 107.30 75.96 118.04 126.55 Observations 1305 1305 1305 1305 890 1305 1305 1305

Note: The mean, median, maximum and minimum are in basis points.Source: Bloomberg and author’s own calculations.

2 For calculating the bond credit spread, the generic USD bond yield from the emerging market’s sovereign is used as the risky

bond, while the generic USD treasury yield is used as the risk-free bond (both with 5 years maturity).3 The CDS spreads are daily published reference spreads calculated by Bloomberg (based on actual trades and outstanding

quotes).4 Countries for which both the generic bond- and CDS spread are available, are included in the sample.5 No VECM is estimated for Venezuela, as a cointegration relationship is a prerequisite for using the VECM framework.


HAS1 =

22

12 - 12

2

22

22

12 - 2 1 2 12 + 1

222

HAS2 =

2 1 - 1121

2

22

12 - 2 1 2 12 + 1

222

(2)

In these equations, σ1, σ12 and σ2 form the covariance matrix of the residuals of the VECM (equation 1). These measures are a reflection of the contribution to price-discovery; if it is close to 1, the CDS market leads price discovery and the bond market follows in order to correct pricing errors; when it is close to 1/2 , both markets have an equal contribution to the process. The results (see table 2) clearly show that the bond market is leading in most emerging markets (in contrast to the markets in the EU or the USA), with the exception of Turkey. An explanation of these results could be that in emerging markets local investors are mainly active in the bond market (Sapriza et al., 2009), which gives this market an informational advantage.

Drivers of the CDS spread

A third question concerns the drivers of the CDS spread6, which is studied by a panel data analysis. The estimated regressions (variables following from existing literature) are the following:

CDS CRIi,t LIQi,t 3Mti,t 1 2 3FF t i,t i,t4VIX 5CONT RISISt (3)

CDSi,t = + 1 CRIi,t + 2 LIQi,t + 3 FF3Mt +

4 VIXt + 5 CONTi,t + CRISISt + i,t (4)

In equation 3 and 4 the variables are the following (details will be discussed below):

• CDSi,t = CDS spread in basis points for country i at time t;

• CRIi,t = Credit rating index for country i at time t;• LIQi,t = CDS entity specific illiquidity (bid-ask spread

in basis points) for country i at time t;• FF3Mt = Federal Funds 3 months future yield in basis

points at time t (global liquidity);• VIXt = Volatility Index of S&P 500 (VIX) in annualized

variance at time t (global risk);• CONTi,t = Contagion index (to country i); index is a

credit rating index of the region;• CRISISt = Crisis dummy, equals 1 after the default of

Lehman Brothers (Sept. 15, 2008).

The equations are estimated using a pooled regression and a regression with fixed effects. The necessity of the country-fixed effects are tested using redundant fixed effects tests. The country-fixed effects were significant for the level estimation, but not for the estimation in first differences. In order to remove serial autocorrelation, AR-processes are added in the regression. Finally the non-significant variables are removed (starting with the least significant) until all variables in the regression are significant. As most variables in equation 3 are non-stationary, panel cointegration tests are performed to avoid spurious regressions.

The results of the original and the final estimation can be found in table 3 and 4. The most interesting results are

Econometrics

Table 2. VECM estimates and information measures (based on equations 1 and 2).

Error Correction Coefficients Residuals Covariance Matrix Information Measures

Country λ1 t-stat λ2 t-stat σ12 σ2

2 σ12 GG H1 H2

Brazil -0.0439 -4.15126*** 0.01519 2.19785** 110.079 47.0715 1.38795 0.25718 0.21542 0.23148China -0.0203 -4.38366*** 0.022 2.13097** 22.2412 110.809 6.29978 0.52039 0.17099 0.27637Colombia -0.0471 -5.08104*** 0.0131 1.85623** 106.199 61.5921 -5.8293 0.21766 0.12284 0.07956Mexico -0.0418 -4.05223*** 0.0127 1.49553* 121.197 82.1788 2.65061 0.23307 0.11777 0.13542Peru -0.0536 -4.94851*** 0.02349 2.91779*** 146.99 81.2156 -10.308 0.30472 0.27868 0.1984Philippines -0.0559 -5.89394*** 0.02173 2.87295*** 129.189 82.2207 17.7777 0.27999 0.16399 0.3098Turkey -0.019 -1.61724* 0.06468 5.22230*** 140.501 155.648 72.682 0.77266 0.54162 0.94806Average -0.0402 - 0.0247 - - - - 0.36938 0.23019 0.3113

Significance of error correction coefficients based on a one-sided t-test.Significance level: *** 1% ** 5% * 10%

6 As no bid-ask spread is available for generic bond spreads, it is chosen to examine the drivers of the CDS spread instead of

the bond credit spread. Please notice that it expected that the results will also be valid for the bond market (due to arbitrage).


Econometrics

Table 3. Panel regression results in levels; dependent variable: CDS (based on equation 3).

Coefficient t-Statistic Coefficient t-Statistic

Constant 403.5882*** 33.88628 243.378*** 4.912416CRIi,t -30.2883*** 46.3065LIQi,t 14.15485*** 151.029 FF3Mt -0.30995*** -18.9035 -0.30363*** -6.78699VIXt 0.887939*** 5.230046 2.301031*** 37.22779CONTi,t 0.760983 0.847565 CRISISt -47.9249*** -6.65318 11.46453** 2.451856AR(1) 1.328701*** 136.7235AR(2) -0.33163*** -34.1294 Country fixed effects no yes Period fixed effects no no R-squared 0.794874 0.998376 Adjusted R-squared 0.794751 0.998374 F-statistic 6466.803 473704.8 Prob(F-statistic) 0 0 Durbin-Watson stat 0.367129 2.013002 Observations 10020 9258

Significance levels: *** 1% ** 5% * 10%

Table 4. Panel regression results in first differences; dependent variable: ∆CDS (based on equation 4).

Coefficient t-Statistic Coefficient t-Statistic

Constant 0.001284 0.006527 -0.04421 -0.20673∆CRIi.t -7.861466** -2.01144

∆LIQi.t 0.105287*** 4.713646

∆VIXt 2.71449*** 40.06784 2.309001*** 37.3933∆FF3Mt -0.346794*** -7.332096 -0.32144*** -7.11852∆CONTi.t 1.495995 0.228595

CRISISt 0.140588 0.487958

AR(1) 0.331793*** 34.16194

Country fixed effects no no

Period fixed effects no no

R-squared 0.166202 0.251002

Adjusted R-squared 0.165682 0.250759 F-statistic 319.5935 1033.722 Prob(F-statistic) 0 0

Durbin-Watson stat 1.279254 2.013089 Observations 9627 9258

Significance levels: *** 1% ** 5% * 10%


Econometrics

that only the global variables (VIX, FF3M and CRISIS) are significant after adding the AR-processes, and that e.g. the influence of the credit rating disappears after the inclusion of the past prices. The first observation can be explained by the diversification theory; the entity-specific variables are diversified out and so are not relevant anymore. The credit ratings do not seem to reveal any new information to the financial markets. This is quite logical, as sovereign credit ratings are based on the same (mostly publicly available) data. Therefore the discussions surrounding the role of credit rating agencies in the European sovereign debt crisis are exaggerated. Basically a change in a credit rating is not much more than an indicator for further analysis. Finally, as the graphs showed data clustering, GARCH regressions are estimated for the individual countries. In all these estimations, the ARCH and GARCH term are significant. Moreover, the GARCH results of the individual countries are generally in line with the results of the panel data studies, so confirming each others’ outcome.

Conclusion

The above mentioned results show that bond- and CDS markets contain information on the creditworthiness of a sovereign entity. Both markets price the credit risk equally, however the bond market is somewhat faster with the price discovery process. The study of the underlying drivers of the CDS spreads show that caution should be taken in interpreting the spreads as information source. Therefore the spreads in the financial markets provide merely an ordinal ranking of the creditworthiness, instead of providing an absolute value of the creditworthiness (e.g. a probability of default). It indicates that a comparison of the spread of the entity to its peer group can give valuable information about how the financial market reviews the current creditworthiness of the sovereign. Furthermore the empirical results of this paper indicate that when the spread of an entity has a sudden jump, it should be a reason for further investigation (whether it is due to global factors or to some newly available information). Summarized, this paper agrees with the view of the credit rating agencies that market indicators should not be used as solely source of information, but should rather be used besides fundamental analysis as a secondary resource.

References

Duffie, D. (1999). Credit swap valuation. Financial Analysts Journal, 55, (1), pp. 73-87.

Gonzalo, J. and C. Granger (1995). Estimation of common long-memory components in cointegrated systems. Journal of Business & Economic Statistics, 13, (1), pp. 27-35.

Hasbrouck, J. (1995). One security, many markets: determining the contributions to price discovery. The Journal of Finance, 50, (4), pp. 1175-1199.


Actuarial Sciences

Developments on the interest rate market

The development of the interest rate can be seen in figure 1. We see that the interest rate term structure2 of a few years ago was relatively flat and that the long term interest rate was around 4 to 5 percent. Since 2009 the interest rate dropped. Especially the short term interest rate declined strongly due to the expansionary monetary policy of the European Central Bank. The 10-year interest rate was 3 percent at the end of 2010, while it was about 4.5 percent two years earlier. We see a similar decline when we look at the 30-year interest rate.

Influence of the interest rate on the funding level

The funding level of a pension fund is the ratio between the market-value of the assets and the market-value of the liabilities. Future liabilities are discounted with an interest rate that has a time-to-maturity that corresponds with the time-to-maturity of the liabilities. If interest rates decline, the present value of the pension liabilities will increase and therefore the funding level will decrease. When a pension fund has more long-term liabilities this effect will be greater. The average funding level drastically declined due to the credit crisis. Figure 2 contains an overview made by the Dutch Central Bank (hereafter: DNB), in which the estimated funding level of all Dutch pension funds is shown between the first quarter of 2007 until the third quarter of 2010.

Before the credit crisis the average funding level was well above 120 percent (the funding level at which pension funds are sufficiently funded), whereas the funding level was even below 100 percent in some quarters of 2008, 2009 and 2010. This is below the minimally required funding level of 105 percent in the Netherlands. In the beginning of 2009 and in mid-2010 about 90 percent of the participants in Dutch pension funds were in this situation.

The decline in the funding level of the Dutch pension funds has several causes:

• A strong decline in the value of investment portfolios. The value of assets dropped in a lot of asset classes;

• A strong decline in the interest rate caused a strong increase in the market-value of the liabilities;

Under the current rules pension funds must value their pension liabilities using market-value interest rates. This is in contrary to the fixed interest rate that was used before. In this article we explain which effects market-value interest rates have on the Dutch pension market1.

by: Dirk Korbee and Arjen Pasma

The Effect of Interest Rate Changes on the Dutch Pension Market

Dirk Korbee and Arjen PasmaDirk Korbee is a Director in the Actuarial & Employee Benefits practice of Deloitte in the Netherlands. He specializes in strategic pension advisory and post-merger integration advisory to corporate clients. Dirk is an actuary and member of the Dutch Actuarial Association and holds a Master’s Degree in Econometrics and Actuarial Sciences.

Arjen Pasma is a Director in the Financial Risk Management practice of Deloitte in the Netherlands. He specializes in risk management, investment process and model validation advisory to financial institutions. Arjen is a CFA charterholder and holds a Master’s Degree in Econometrics.

1 For this article the website www.pensioenopbouwen.

nl/extra-kosten-bij-pensioenoverdracht-voor-nieuwe-

werkgever has been used.2 This is the Eur Government Strips AAA BPV Curve (source:

Bloomberg L.L.P.)

Figure 1. Development of the risk-free interest rate from

December 2005 until 2010.


Actuarial Sciences

• The mortality tables were adjusted considerably. Life expectancy increased more than expected, so pension funds have to grant pension over a longer period of time.

Decreasing the influence of the interest rate

The funding level of a pension fund strongly depends on the developments of interest rates. To decrease this dependency, pension funds can adjust their asset mix accordingly. This can be done by applying duration matching4, where the duration of the assets is matched with the duration of the liabilities. However, in practice, it proves to be impossible for pension funds to obtain a complete match using duration matching, due to the high duration of the pension liabilities of most pension funds. Such a high duration is difficult to match with investments consisting of only bonds and other fixed-return assets.

Pension funds can also choose to invest in other interest rate derivatives (swaps, swaptions) in order to further reduce the interest rate risks. These are common financial products now, but for such ‘over-the-counter’ contracts there are other points of interest like counter-party risk and the collateral that is given.

However, with the current average funding level it is often not possible to entirely match the duration of the average pension fund. Thus the chance on investment returns remains, with which future indexation could be financed. The reduction of risk therefore leads to pressure on the (conditional) indexation and the associated position in the indexation label and the indexation matrix.

Influence of current interest rates on collective insurance contracts and value transfers

Pension funds that operate pension schemes that qualify as Defined Benefit (DB)-schemes guarantee (to a certain extent) a yearly payment starting at the pensionable age. Pension funds or companies that would like to insure their pension liabilities collectively at an insurer will have to pay higher premiums due to the lower interest rates. In the past insurers guaranteed future pension payments using a fixed interest rate of 4 percent. Currently, insurers use a fixed interest rate between 3 and 3.5 percent. In order to guarantee the same pension entitlement, the insurer is forced to increase premiums, while a higher risk surcharge is needed as well.

Interest rate developments also have consequences for individual value transfers in a pension scheme at an insurer. Such value transfers can occur when an employee switches jobs and transfers the accrued pension rights to the new employer. The pension rights that the employee brings to the new employer are valued with a fixed interest rate that is determined yearly. This percentage has also declined to approximately 3 percent due to the recent developments on the interest rate market. This may lead to additional costs for the old employer. After all, the value of the accrued pension rights has increased compared to the insured value in the contract and the new employer will have to receive this (higher) amount to buy the accrued pension rights at the insurer or to insure it at a pension fund. The employee has a legal right of a value transfer of pension rights and as such the (old) employer cannot prevent these costs of a leaving employee.

Conclusion

The developments of the interest rates had major consequences for the value of pension rights. Because the interest rates are on a historically low level, it is harder (and therefore more expensive) to realize the pension rights. As a consequence the funding levels of pension funds decreased and the premiums for pension insurances increased. In the meantime, the funding levels of pension funds are recovering, especially due to recovery of the word-wide financial markets. Furthermore, there is an increase of the relevant interest rate of 1 percent point since the absolute low around august 2010. Whether the interest rate will keep increasing is hard to predict. Moreover, it will take until 2012 before we are rid of the current interest rate for individual value transfers.

3 Source: http:// www.statistics.dnb.nl/index.cgi?lang=nl& todo=Pen2, tabel 8.8: Geraamde dekkingsgraad van pensioen-

fondsen.4 Duration is a measure for interest rate sensitivity and measures the impact of an increase of 1 percent of the yield curve on

the value of the assets and liabilities of the pension fund.

Figure 2. Estimated funding levels of the Dutch pension

funds3.


Econometrics

Introduction

Due to nonresponse, the sample size is smaller than expected. This leads to less accurate, but still valid estimates of population characteristics. This problem can be solved by increasing the initial sample size in order to meet precision levels or power analyses. A far more serious problem that may be caused by nonresponse is that estimates of population characteristics are biased. This situation occurs if, due to nonresponse, some groups in the population are over- or underrepresented, and these groups behave differently with respect to the topics of the survey. Consequently, this will lead to wrong conclusions.

In this article, we give an introduction to indicators that can be used to assess and evaulate the impact of nonresponse, so-called R-indicators. The ‘R’ stands for representativity. The R-indicator measures whether or not the survey response is representative. If the indicator shows a deviation from representativity, there is a serious risk of biased estimates. If it indicates that the survey response is representative, estimates have a smaller risk of being biased. The R-indicator was originally proposed by Schouten, Cobben and Bethlehem (2009). We also show how the indicator can be applied to practical survey situations.

The R-indicator

The R-indicator is computed as a transformation of the variance of estimated response probabilities to the [0,1] interval. A value equal to 1 implies representative response. A value equal to 0 implies a maximal deviation from representative response.

Suppose the estimated response probabilities for the n elements in the sample are denoted by ρ1, ρ2, …, ρnand the sample design inclusion weights are denoted by

dd ,, 21 ... nd, . The design weights are the inverse of the probabilities that a population unit is contained in the survey sample. Then the R-indicator is computed as

, (1)

with

the weighted sample mean of the estimated response probabilities and N the size of the population.

The R-indicator thus reflects the overall variation of individual probabilities to respond to a survey. It is also possible to break down this variation into components that are attributable to different characteristics of the sample elements. Such indicators are called partial R-indicators, see Bethlehem and Schouten (2011). There are two types of partial R-indicators: the unconditional partial R-indicator and the conditional partial R-indicator.

The unconditional partial R-indicator measures how large the variation of the response probabilities is between the categories of a variable. The larger the between-category variation is, the stronger the relationship with the response behaviour.

Conditional partial R-indicators can only be computed for variables that are included in the response model. The conditional partial R-indicator measures the importance of variables in explaining the lack of representativity,

Nonresponse in sample surveys is the phenomenon that elements (e.g. businesses, persons, or households) selected in the sample do not provide the requested information, or that the provided information is useless. The situation in which all requested information on an element is missing (the questionnaire remains empty), is called unit nonresponse. When only answers on some questions are missing, this is referred to as item nonresponse. In this article we focus on the analysis of unit nonresponse and its impact on the quality of survey statistics.

by: Jelke Bethlehem, Fannie Cobben and Barry Schouten


Jelke Bethlehem, Fannie Cobben and Barry Schouten

Prof. dr. Jelke Bethlehem, dr. Fannie Cobben and dr. ir. Barry Schouten are all employed as survey methodologists at the Department of Methodology and Quality of Statistics Netherlands. They have been working on nonresponse related research issues for several years, and recently published the Handbook on Nonresponse in Household Surveys at Wiley, NY.

( )∑=

−−

−=−=n

iiid

NSR

1

2

1121)(21 ρρρ

∑=

=n

iiid

N 1

1 ρρ


Econometrics

taking into account the other variables. Two variables may be important for explaining response behaviour, but if they measure the same aspect of response behaviour, just one variable is sufficient for explaining response and the other variable can be ignored. In other words: conditional partial R-indicators only measure ‘pure’ effects of variables. These are effects that are not accounted for by other variables.

Applications of the R-indicator

The R-indicator and the partial R-indicators are based on response probabilities. These are unknown and need to be estimated using a pre-defined set of auxiliary variables. The indicators therefore depend on the auxiliary variables.

The indicators introduced in this article may serve a number of purposes:

1. To compare the quality of the response to different surveys that share the same target population;

2. To compare the quality of the response to a survey longitudinally, e.g. montly, quarterly or annually;

3. To monitor the quality of the response to a survey during data collection, e.g. after various days, weeks or months of fieldwork;

4. To improve the quality of the response by targeting groups that cause deviations from representative response and by tailoring survey designs.

The selection of auxiliary variables depends on the intended use of the R-indicator and, obviously, on the availability of auxiliary variables.

In this paragraph, two purposes are described based on applications within Statistics Netherlands: Monitoring the quality of the response during fieldwork for the Short Term Statistics business survey and a comparison of the quality of the response in time for the Labour Force Survey.

Quality of the response during fieldwork: A business survey

The monthly Short Term Statistics (STS) survey was conducted by Statistics Netherlands in 2007. Data are considered on sampled businesses in two major categories of economic activity of interest: Retail industry (sample size = 93,799) and Manufacturing industry (sample size = 64,413). Despite being a mandatory survey, nonresponse occurs, with possible reasons including lack of awareness of the mandatory nature of the survey and forgetting or

refusing to respond. More importantly, response to the STS may be too late to be included in STS statistics. Estimates from the STS survey are needed 30 days after the end of the reference month, and between three and five days is needed to process, edit, impute and aggregate survey data. For the accuracy of STS statistics it is imperative to assess the impact of nonresponse after different periods of data collection, especially between 25 and 30 days of data collection. The question that we would like to answer: Is response sufficiently representative after 25 days?

A summary of response rates after varying periods is presented in Table 1, from which we can conclude that between 25 and 30 days the response rates go up by approximately 6%.

In order to investigate the impact of the length of fieldwork, the R-indicators and partial R-indicators were calculated after different time periods. Auxiliary variables used to define the indicators were: type of economic activity, business size in terms of numbers of employees and total revenue reported to Tax Office in previous year.

Table 2 contains estimated R-indicators. The two sectors show different patterns of the R-indicators over time. While the R-indicator for Manufacturing grows steadily over time from 0.878 to 0.931, the R-indicator for Retail is very stable.

Table 3 contains the unconditional and conditional partial R-indicators for type of economic activity after different periods of time. Three observations can be made. First, the difference between the unconditional and conditional indicators is small. Thus, the impact of business type is not removed by controlling for business size and revenue. Second, the values of the indicators for Manufacturing are considerably larger. Given that the R-indicators are similar in size, and, hence, the

Table 1. Summary of response rates in the Short Term Statistics business survey.

Time Retail Industry

15 days 49.5% 48.8%25 days 71.4% 73.1%26 days 72.9% 74.4%27 days 74.5% 75.8%28 days 75.7% 76.9%29 days 76.9% 77.9%30 days 78.0% 78.7%45 days 85.8% 85.7%60 days 88.2% 88.3%

Table 2. R-indicators for Retail and Manufacturing after different data collection periods.

15d 25d 26d 27d 28d 29d 30d 45d 60d

Retail 0.890 0.887 0.886 0.884 0.883 0.882 0.881 0.887 0.893Manufacturing 0.878 0.891 0.894 0.891 0.897 0.901 0.903 0.928 0.931


Econometrics

variation in response probabilities is also similar, this means that economic activity has a stronger impact on representativeness for Manufacturing than for Retail. This impact gradually diminishes with time. After 45 days of data collection the partial indicators for Retail and Manufacturing are comparable in size. Third, the impact of business type is stable over time for Retail. When extra response comes in, there is no change in representativeness with respect to business type.

From these observations we conclude that there is the potential to improve representativeness for Industry by speeding up response for some types of economic activity.

The representativity of the Labour Force Survey in time

The first round of the Dutch Labour Force Survey (LFS) was redesigned from a single mode survey to a mixed-mode survey. Until 2009 the first round of the LFS was a Computer Assisted Personal Interview (CAPI) survey. In 2010 the first round of the LFS became a mix of CAPI and Computer Assisted Telephone Interview (CATI). Households with a registered telephone were approached by CATI and all other households were approached by CAPI. This paragraph presents the R-indicators for the first round of the LFS for the years 2006, 2008, 2009 and 2010. For 2010 both the R-indicators for the old and the new survey design are shown. Table 4 presents response rates and R-indicators for the LFS in the various years. The model used to estimate individual response probabilities was the same for all years. The auxiliary variables used in the model are: degree of urbanization, age, type of

household, paid job, house value, and ethnicity.From Table 4 it can be concluded that response

rate dropped gradually over the years. However, the R-indicator remained stable. The R-indicator had the highest value for 2008. This value is significantly higher than that of all other years, except for the new design in 2010. The redesign of the LFS did not affect the representativity of the response with respect to the six auxiliary variables, despite of the low response rate in the new design.

To obtain more insight into the differences over the years, the R-indicator and partial R-indicators were computed for making contact and for overall response. A reduced set of auxiliary variables was used: age, house value, and paid job. Table 5 presents the indicators for 2006 and 2008.

It can be concluded from Table 5 that with respect to making contact, 2006 and 2008 were very similar. The contact rate, the R-indicator for contact and the partial R-indicator for contact are all very similar for 2006 and 2008. For overall response however, the values for the partical R-indicators changed. The impact of age became much smaller in 2008, while the impact of house value increased. The values of the conditional partial R-indicators for age, house value, and paid job suggest that these three variables are unrelated to contact and overall response.

Table 3. Unconditional and conditional partial R-indi-cators ecomic activity (PU = unconditional and PC = conditional).

Days Retail Industry PU PC PU PC

15 0.017 0.016 0.047 0.04325 0.013 0.014 0.037 0.03326 0.013 0.013 0.035 0.03127 0.014 0.012 0.033 0.02928 0.014 0.012 0.032 0.02829 0.013 0.012 0.031 0.02730 0.013 0.012 0.029 0.02545 0.014 0.011 0.017 0.01560 0.013 0.011 0.015 0.013

Table 4. Response rates and R-indicators for the LFS in the period 2006 – 2010.

2006 2008 2009 2010 (old) 2010 (new)

Response rate 63.1% 62.1% 61.9% 59.5% 53.9%R-indicator 0.840 0.863 0.845 0.849 0.852C.I. 0.835-0.845 0.858-0.868 0.840-0.851 0.841-0.856 0.845-0.860

Table 5. Contact and overall response rates, R-indica-tors and partial R-indicators (PU = unconditional and PC = conditional) for the first round of the LFS in 2006 and 2008.

Contact Response

2006 2008 2006 2008

Response rate 94.1% 94.9% 63.1% 62.1%R-indicator 0.943 0.940 0.889 0.884

PU Age 0.021 0.021 0.033 0.013House value 0.021 0.021 0.043 0.052Paid job 0.002 0.002 0.019 0.021

PC Age 0.019 0.019 0.031 0.017House value 0.021 0.021 0.036 0.050Paid job 0.002 0.002 0.024 0.023

Je kunt een land pas besturen als je de cijfers kent.

Zowel de overheid als het bedrijfsleven nemen talloze beslissingen die gebaseerd zijn op cijfers van het CBS. Onze medewerkers rapporteren niet alleen over de Nederlandse economie, maar ook over de internationale handel, de volksgezondheid, de verkeersveiligheid, de bevolking, het onderwijs en veel andere thema’s. Al onze cijfers staan op www.cbs.nl. Kijk voor meer informatie ook op www.werkenbijhetcbs.nl

In 2010 waren er bijna 1,5 miljoen melkkoeien op 19,8 duizend boerderijen.

Nederlanders wonen gemiddeld 5,3 kilometer van het dichtstbijzijnde

ziekenhuis.

In 2010 was de omzet in de horeca bijna 1 procent lager dan een jaar eerder.

In 2040 telt Nederland volgens de CBS-prognose 17,8 miljoen inwoners;

ruim één miljoen meer dan nu.

Met 3,9 procent was Zeeland de provincie met de laagste werk-

loosheid in 2010.

Twee procent van de huishoudens had begin 2010 een vermogen van

1 miljoen euro of meer.

De Nederlandse economie groeide in 2010 met 1,7 procent.

In 2010 bedroeg de in� atie 1,3 procent.

In 2010 telde Nederland 343 tomatentelers.

In Nederland wonen ruim 4,9 miljoen jongeren in de leeftijd

van 0 tot 25 jaar.

Op 1 januari 2011 telde Nederland 418 gemeenten, dertien minder

dan in 2010.

Nederland telde in 2010 gemiddeld 426 duizend werklozen.

In 2010 exporteerde Nederland voor ruim 370 miljard euro aan goederen; 61 miljard euro meer dan in 2009.


Econometrics

References

Bethlehem, J. and B. Schouten (2011). “Nonresponse analysis with the R-indicator.” Discussion paper, BPA-nr. DMV-2011-06-20-JBTM-BSTN, available at www.cbs.nl.

Schouten, B., F. Cobben and J.G. Bethlehem (2009). “Indicators for the Representativeness of Survey Response.” Survey Methodology, 35, pp. 101-113.


Econometrics

Introduction

This paper discusses some of the key ingredients of a robust and reliable approach to price variation estimation over short intraday horizons what is referred to spot volatility or variance. For details, see Bos, Janus, and Koopman (2009), of which we describe the most important results here. With the spot volatility estimates obtained from high frequency data we can track variation of prices minute-by-minute. Importantly, the spot volatility estimates also allow to carry out testing for the presence of jumps at high frequencies or study the origin of these jumps. Volatility and jumps are two fundamentally different risks with their own implications for financial economics, like risk hedging, option pricing etc. There has therefore been a growing interest in providing test statistics designed to detect jumps in asset prices at high frequencies, as initiated by Barndorff-Nielsen and Shephard (2006).

The econometrics of high frequency data encounters numerous challenges to correctly deal with this type of data. The key challenge is to account simultaneously for recurring daily variance patterns, jumps, leverage effects, microstructure noise and price discreteness. In the current note, we present an approach that allows to extract spot volatility with a minimum set of assumptions that largely agree with current literature on high frequency

econometrics. We present the general setup in the next section, followed by, in order, the theory behind the jump test, an empirical study, and concluding remarks.

General setup

For the modeling of asset prices in continuous-time, the standard model is a jump-diffusion process. The efficient but unobserved log price process Xt is assumed to follow a Brownian semi-martingale plus jumps defined as

d d d d ,t t t t t t tX t p W Nμ σ κ= + + 0,t ≥ (1)

where tμ is the drift coefficient (here assumed to be zero), 0tσ > is the stochastic part of spot volatility, 0tp > is the

deterministic periodic part of volatility, Wt is a standard Brownian motion, tκ is the random jump size with mean

( )tκμ and variance 2 ( )tκσ and Nt is a counting process that represents the number of jumps in the price path up to time t. A leverage effect can be incorporated by allowing for negative correlation between Wt and tσ .

In practice the efficient price Xt is latent and we rather observe at times ti (log) price

itY ,

,

i i it t tY X ε= + 0 10 ... 1,nt t t= < < < = (2)

where it

ε represents market microstructure noise with [ ] 0,

itE ε = [ ] 0

i jt tE ε ε = for i j≠ and 2 2[ ]it

E ε ϖ= . It is also assumed that the efficient price and the microstructure noise are independent of each other at all lags and leads, i.e. [ ] 0

i jt tE X ε = for any i, j. For simplicity, it is assumed that microstructure noise follows a Gaussian distribution, but this assumption can be also relaxed. In testing for jumps, it is assumed that variance of microstructure noise shares similar diurnal pattern as the variation of efficient innovations.

The key challenge is to estimate the spot volatility tσ of the efficient (unobservable) price Xt. This in turn means

In this note we present a method to estimate the volatility at any time within a trading day using high frequency price data. The method is not hindered by the occurrence of (infrequent) jumps, (frequent) microstructure noise, daily recurring patterns in the variance, or leverage effects. The resulting spot volatility path allows to track variation of prices at short intraday horizons, or to test for jump effects related to e.g. news announcements. We present an empirical illustration of spot volatility estimation and jump testing for the intraday EUR/USD exchange rate.

by: Charles S. Bos and Pawel Janus

Spot Volatility of High Frequency Data

Charles S. Bos and Pawel Janus Charles Bos obtained a PhD in Econometrics at the Erasmus University Rotterdam in 2001. Afterwards, he worked as a Research Officer at Oxford University, and later as a researcher and assistant professor at the Econometrics department of VU University Amsterdam. At present his research focuses on time series modeling of financial and macro-series, both at low and high frequencies.

Paweł Janus graduated from the MPhil program at the Tinbergen Institute, and now he is a PhD candidate in the time series econometrics group at the VU University Amsterdam. During his PhD studies he visited Stanford University Department of Economics. His PhD research focuses on measuring and modeling financial market volatilities and dependencies using both high and low frequency data.

voor wie?Je zit in de laatste fase van je studie HBO of WO economie, rechten of econometrie. Of je doet een technische of sociale studie en hebt affiniteit met de financiële sector. Daarnaast ben je vasthoudend, indringend en een echte teamspeler.

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Econometrics

that we need to estimate the deterministic multiplier pt, while being robust against possible jumps tκ . Moreover, it follows from (2) that extraction of the efficient price variation must eliminate excess variation due to noise effects; this is crucial because for higher frequencies the variation due to noise ϖ dominates the stochastic variation of efficient innovations dt tWσ .

Spot Volatility and Jump Testing

Stochastic variation

In an ideal frictionless market, without jumps or microstructure noise, and with no intraday seasonality, the efficient price increment is conditionally normally distributed with mean zero and variance 2

itσ Δ, with

1i it t −Δ = − . In this case, the spot variance at time ti can be consistently estimated by normalized realized variance

1

22ˆ ( ) ,jji

n

i

t t tj i hn

n X Xh

σ−

= −

= −∑ (3)

where nh hn= with 0h > and nh →∞ satisfying / 0nh n → . However, the presence of microstructure noise (due to bid-ask bounce, decimal misplacements etc.) and of jumps calls forth a robust approach as the estimator (3) based on realized variance becomes upward biased. For our purpose, we adopt an approach that simultaneously robustifies against microstructure noise and jumps. We apply the pre-averaged bipower variation, see Jacod et al. (2009); Podolskij and Vetter (2009), which is then normalized to provide the spot measure. The resulting spot variance estimator is given by

2 1/2 222 11

221

ˆˆ | || | ,n

nin

i k

kjjtj i hn

n Y Yh

ϕμσ ϖ

ϕ ϕ

− −

+= −

= −Θ Θ∑ (4)

which effectively is the bipower variation computed from pre-averaged returns

1

1

1( / )( ),

n

i j i j

k

i n t tj

Y g j k Y Y+ + −

−

=

= −∑ (5)

and adapted for the microstructure noise variance

1 1 2

2

2

1ˆ ( )( ),1 i i i i

n

t t t ti

Y Y Y Yn

ϖ− − −

=

= − − −− ∑

which is calculated from the (negative) first order autocorrelation of the returns. Here nk n= Θ ,

( ) min( ,1 )g z z z= − , 1 2 /μ π= , 1 1ϕ = and 2ϕ = 112.

The parameter Θ determines the window over which the observed price increments are averaged using the

function g(z) in (5), and in most applications [1/ 4,1]Θ∈ is a good choice.

Pre-averaging the returns lowers the effect of the microstructure noise, whereas using non-overlapping pre-averaged returns | || |

nj j kY Y + robustifies the estimator against possible jumps. The second term proportional to 2ϖ̂ bias-corrects for any remaining microstructure frictions.

Note that the spot volatility is estimated using a window of width hn. A longer window gives a more precise, but possibly also more biased estimator. Our simulations studies with various variance specifications suggest a choice of 3/ 4

nh n= is often an optimal choice.

Intraday periodic variation

The intraday seasonal patterns in return variation are mostly due to the opening, lunch-break and closing of the own market and other related markets, see Andersen and Bollerslev (1997). Identification of the periodic patterns implies that we can decompose the total spot volatility into a stochastic variable tσ and a deterministic multiplier pt. It is natural to assume that pt equals one on average implying that pt is higher (lower) than unity when intraday trading activity due to periodic effects increases (decreases). It is also natural to assume that the shape of pt is the same for each trading day (or the same across weekdays). The general idea of diurnal pattern extraction is to robustly smooth the series of variances of returns over the same intraday time interval across all days in the sample. Let d denote the dth day in the sample, 1,..., ,d D= we define the cross-sectional variance as

1

1

2 22 1

2 21 1

( ) /,

( ) /i i

i

j j

Dd t d t dd

t n Dd t d t dj d

n Y Ys

Y Y

σ

σ−

−

+ +=

+ += =

−=

−

∑∑ ∑

which is normalized to have mean one. Note how the price increments are adapted for the current level of the daily volatility 2

dσ . Even though the cross-sectional variances are often used in the literature as estimate of diurnal pattern, it is a noisy measure and very sensitive to all sort of outliers as it relies on squared returns. Instead, we propose to smooth the series of cross-sectional variances using

2

1

ˆ ˆ ,i j

n

t ij tj

p sω=

= ∑ where ijω are weights stemming from a robustified exponentially weighted moving average approach (Bos et al., 2009).

Jump testing

In a frictionless market, the efficient price increment is conditionally normally distributed with mean zero and variance 2

itσ Δ implying that the standardized price

increment is standard normally distributed. This provides


Econometrics

a test statistic to detect jumps over the interval 1( , ]i it t− . Note that this type of jump testing will have to account for intraday seasonal patterns as well as microstructure noise. In the setting outlined in (1)-(2), the observed price increment

1i it tY Y−

− in the absence of jumps (as under the null) over the interval 1( , ]i it t− conditionally normal with mean zero and variance 2 2 2 2 22

i i i it t t tv p pσ ϖ= Δ + . The resulting test statistic is given by

1i i

i

t t

t

Y Yv

−−

~ N(0,1).

If a jump occurs over the interval 1( , ]i it t− , the price increment should deviate significantly from the normal distribution. It is important to note that jump detection in the presence of microstructure noise depends on the magnitude of price contamination. When the variance of microstructure noise increases, small jumps are of course more difficult to detect.

Empirical illustration

Data description

We present an empirical study of the EUR/USD exchange rate data from July 2 to December 31, 2007 with 131 trading days. We construct a series of Δ = 1min returns. The returns on EUR/USD exchange rate are non-normal as judged by excessive kurtosis and non-zero skewness. The non-normality can be explained by time-varying volatility (both stochastic and deterministic due to intraday seasonalities) and/or presence of jumps. There is some microstructure noise in this data which is diagnosed by the negative first order autocorrelation.

Figure 1 presents autocorrelation functions (ACF) of raw returns

1i it tY Y−

− (upper panels, a) and after adapting for intraday seasonality

1( ) /

i i it t tY Y p−

− (lower panels, b). The left panels i) show the ACF for 5 days, while right panels ii) present the part of ACF corresponding to daily lags for all days. The upper panels indicate clearly that autocorrelations are U-shaped and persistent. The lower panels show that adapting for intraday seasonality removes much of the systematic persistence and returns are effectively left with only stochastic variance 2

tσ .

2007-7-1 7-8 7-15 7-22 7-29 8-5 8-12 8-19 8-26 9-2 9-9 9-16 9-23 9-30 10-7 10-14 10-21 10-28 11-4 11-11 11-18 11-25 12-2 12-9 12-16 12-23-0.2

-0.1

0.0

0.1

0.2i)

(4) (3)

2007-7-1 7-8 7-15 7-22 7-29 8-5 8-12 8-19 8-26 9-2 9-9 9-16 9-23 9-30 10-7 10-14 10-21 10-28 11-4 11-11 11-18 11-25 12-2 12-9 12-16 12-23

0.01

0.02

0.03 ii) (4) (3)

Figure 2. EUR/USD returns and spot volatility.

0 1 2 3 4 5

0.00

0.05

0.10

0.15i-a)

0 25 50 75 100 125

0.000

0.025

0.050ii-a)

0 1 2 3 4 5

0.00

0.05

0.10

0.15i-b)

Days 0 25 50 75 100 125

0.000

0.025

0.050ii-b)

Days

Figure 1. Autocorrelation of EUR/USD exchange rate, intradaily i) and between days ii), before a) and after b) adapting for

periodicity.


Econometrics

Jump testing

First, Figure 2 presents returns on EUR/USD exchange rate and the estimated spot volatility path based on our preferred pre-averaged bipower variation measure (4) and realized variance (3) for a reference. Since there is an evidence of microstructure frictions, the spot variance estimator (3) yields an upward bias which has in consequence an adverse impact on jump testing analysis.

On September 5, 2007, jumps contribute around 30% to total price variation, which is relatively much. This specific day corresponds to a day with scheduled macroeconomic announcements relevant for the EUR/USD exchange rate, as listed in Table 1. This day there are 4 jumps detected at 00:44, 07:38, 15:18 and 17:12 at the 1% significance level. At the 5% level, three additional jumps are found at 00:43, 15:19 and 17:10; see panel ii) of Figure 3. These time intervals correspond to high intraday volatility time periods, when markets open or overlap. The morning European news items

were positive for the EUR/USD rate on that day. It is seen from Figure 3 that the EUR/USD rate started to appreciate dramatically in the afternoon when the US readings were much worse than expected; for instance note that consensus for employment change was 80k, while the actual announcement was only 27k. The sizes (in absolute terms) of the detected jumps were from 7 to 10bps (or from 6bps at α = 5%), which corresponds to around 0.07-0.1% change of the fundamental within a 1min interval. When lowering the sampling frequency to e.g. Δ = 15min only 2 jumps are found to be significant, at 15:18 (-15bps) and at 17:12 (42bps) contributing around 50% to the total price variation. In general, the lower the frequency, the lower the power of test to detect jumps.

Conclusion

This article presented briefly how to estimate the spot volatility of high frequency price data. The approach is robust and reliable, and it takes into account stylized facts

Table 1. Important news releases on September 5, 2007

Time Area Event Actual Consensus Previous +/-

08:55 DE PMI Services (Aug) 59.8 58.1 58.5 +09:00 EMU PMI Services (Aug) 58.0 57.9 58.310:00 EMU Retail Sales (MoM) (Jul) 0.4% 0.3% 0.6% +10:00 EMU Retail Sales (YoY) (Jul) 1.3% 1.1% 1.0% +13:15 US Employment Change (Aug) 27k 80k 48k +15:00 US Pending Home Sales (MoM) (Jul) -12.2% -2.0% 5.0% +

Note: The + (-) denotes a positive (negative) reading for the EUR/USD exchange rate. DE - Germany, EMU - European Monetary Union, PMI - Purchasing Manager Index, PCE - Personal Consumption Expenditure. k = 1000.Source: http://www.fxstreet.com/.

00:00 06:00 12:00 18:00 00:00

1.360

1.365

i)

=5% =1%

00:00 06:00 12:00 18:00 00:00

-0.1

0.0

0.1

0.2

0.3

0.4ii) =5% =1%

Figure 3. Panel i) presents the EUR/USD exchange rate in level; ii) EUR/USD returns and signicant jumps at 1% signicance level

marked with circles and at 5% marked with diamonds.


Econometrics

about this type of data like presence of periodic variance patterns, jumps, microstructure effects (including round-off errors) and leverage effects. Our preferred approach is to decompose the spot volatility into two components: stochastic and deterministic-periodic. Such a decomposition leads to better understanding of the sources of stochastic variation. The spot volatility path allows to track variation of prices at short intraday horizons, like minute-by-minute or even more frequently. Importantly, the estimate of spot volatility also allows to test for abnormally large price increments that might occur with some news releases. For instance, we showed that with certain news releases different from the consensus expectation, large jumps occur in the price process causing a considerable part of total price variation. The methodology discussed in this article enables detailed studies of changes of volatility and jump processes which are two fundamentally different sources of risk.

References

Andersen, T. G. and T. Bollerslev (1997). Intraday periodicity and volatility persistence in financial markets. Journal of Empirical Finance 4(2-3), 115–158.

Barndorff-Nielsen, O. E. and N. Shephard (2006). Econometrics of testing for jumps in financial economics using bipower variation. Journal of Financial Econometrics 4(1), 1–30.

Bos, C. S., P. Janus, and S. J. Koopman (2009). Spot variance path estimation and its application to high frequency jump testing. Working paper 2009-110/4, Tinbergen Institute.

Jacod, J., Y. Li, P. A. Mykland, M. Podolskij, and M. Vetter (2009). Microstructure noise in the continuous case: The pre-averaging approach. Stochastic Processes and Their Applications 119(7), 2249–2276.

Podolskij, M. and M. Vetter (2009). Bipower-type estimation in a noisy diffusion setting. Stochastic Processes and Their Applications 119(9), 2803–2831.


Puzzle

Answer to “Two Blondes”

The second blonde knows the number of houses across the street, so she can easily check which of the five possible combinations of ages provides a sum that coincides with that number. But she has not enough information to solve the puzzle yet, so the only two possibilities left are the two combinations of ages that sum up to the same number: 2, 2, 9 and 1, 6, 6.

The fact that there is an oldest daughter is enough to solve the puzzle: the twins cannot be the oldest, so the three daughters are 2, 2 and 9 years old.

Answer to “Bank Teller”

There are several ways to solve this problem, we only provide the solution by simultaneous equations.

Let x be the number of dollars in the check, and y be the number of cents. The original check is for x dollars and y cents. The bank teller gave Ms Smith y dollars and x cents. After buying the newspaper she has y dollars and x − 50 cents. We are also told that after buying the newspaper she has three times the amount of the original check; that is, 3x dollars and 3y cents.

Clearly (y dollars plus x − 50 cents) equals (3x dollars plus 3y cents). Then, bearing in mind that x and y must both be less than 100, we equate dollars and cents.

As −50 ≤ (x − 50) ≤ 49 and 0 ≤ 3y ≤ 297, there is a relatively small number of ways in which we can equate dollars and cents. (If there were many different ways, this whole approach would not be viable.) Clearly, 3y − (x − 50) must be divisible by 100. Further, by the above inequalities, −49 ≤ 3y − (x − 50) ≤ 347, giving us four multiples of 100 to check.

• If 3y − (x − 50) = 0, then we must have 3x = y, giving x = −25/4, y = −75/4.

• If 3y − (x − 50) = 100, then (to balance) we must have 3x − y = −1, giving x = 47/8, y = 149/8.

• If 3y − (x − 50) = 200, then we must have 3x − y = −2, giving x = 18, y = 56.

• If 3y − (x − 50) = 300, then we must have 3x − y = −3, giving x = 241/8, y = 747/8.

There is only one integer solution, so the check was for $18.56.

Hannah’s House Number

Hannah lives in a street with house-numbers ranging from 8 to 100. Jake wants to know at which number Hannah lives.

He asks her: “Is your number larger than 50?” Hannah answers, but lies.

Upon this, Jake asks: “Is your number a multiple of 4?” Hannah answers, but lies again.

Then Jake asks: “Is your number a square?” Hannah answers truthfully.

Upon this, Jake says: “I know your number if you tell me whether the first digit is a 3.” Hannah answers, but now we don’t know whether she lies or speaks the truth.

Thereupon, Jake says at which number he thinks Hannah lives, but (of course) he is wrong. What is Hannah’s real house-number?

The Bitterbal Problem

On a nice summer day, two tourists visit the Dutch city of Amsterdam. During their tour through the center they spot a cosy terrace. They decide to have a drink and, as an appetizer, a portion of hot “bitterballen”. The waiter tells them that the bitterballen can be served in portions of 6, 9, or 20. What is the largest number such that they can not order any combination of the above to achieve exactly the number of bitterballen they want?

Solutions

Solutions to the two puzzles above can be submitted up to November 1st 2011. You can hand them in at the VSAE room (E2.02/04), mail them to [email protected] or send them to VSAE, for the attention of Aenorm puzzle 72, Roetersstraat 11, 1018 WB Amsterdam, Holland. Among the correct submissions, one book token will be won. Solutions can be both in English and Dutch.

On this page you find a few challenging puzzles. Try to solve them and compete for a prize! But first we will provide you with the answers to the puzzles of last edition.


Agenda Agenda

• 22 - 25 August IDEE Week

• September General Members Meeting

• 22 September LEVT

• 29 - 31 August VSAE Introduction Days

• 13 September Monthly drink

• 20 September Actuarial Congress on Solvency II

• 22 September LEVT

• 26 September General Members Meeting

• 4 - 5 October Beroependagen

The last months of the past academic year held some great activities for Kraket. In June, our annual Kraketweekend took place. With a group of 50 students we travelled to MidLaren where we had a great weekend. We went waterskiing, fencing and archering among other things. Then, after the last activity of the academic year: a beachvolleybal tournament and cocktail shake workshop in Zandvoort, a well-deserved holiday took place.

Now with the summer holiday almost over, a new academic year is upon us. With a brand new board and a new enthusiastic group of students, this year can only bring Kraket to even greater heights.

In the upcoming year Kraket will, together with the VSAE, organize the LED 2012. This year’s LED will take place in Amsterdam. In 2012, Kraket will also celebrate its 8th lustrum. Our 40th anniversary will be appropriately celebrated in an action packed week at the end of the academic year.

In the following month we have planned a lot of activities to look forward to. We are confident that the upcoming academic year will bring even more success for Kraket and we hope to see you at one of the activities!

The last few months, it has been a quiet period for the VSAE. After the successful drink on the last day of the academic year, our members enjoyed their summer holidays. Of course, the organization of our upcoming events continued.

Every year, we welcome our new first year students on the VSAE Introduction Days. This year, we will take off to Friesland with fifty freshman. In three days, they will get to know each other and the VSAE and, above all, have a lot of fun.

On the 20th of September, the eleventh edition of the Actuarial Congress will take place in De Rode Hoed in Amsterdam. This year, the congress will be all about Solvency II and Risk Management. Besides presentations of experts on this theme, a risk management game and an ORSA workshop will be part of the program.

The Beroependagen, organized in cooperation with the FSA, will take place on the 4th and 5th of October. Students with a quantitative or financial background can enjoy presentations, workshops, lunches and dinners with leading companies in Hotel Sofitel Amsterdam The Grand.

We have a lot more activities ahead, like our monthly drinks, the National Econometricians Soccer Tournament (LEVT) in Tilburg and the traditional pool tournament in October. We look forward to seeing you there!

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HET FUSIER APPORT VOOR EEN

INTERNATIONALE BIERBROUWER

W W W.GA A AN.NU

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